The field of the invention is systems and methods for magnetic resonance imaging (“MRI”). More particularly, the invention relates to systems and methods for concomitant field correction and compensation when implementing asymmetric gradients during an MRI scan.
According to Maxwell's equations, a magnetic field gradient used for spatial encoding in MRI is always accompanied by spatially variant higher order magnetic fields, which are conventionally termed as “concomitant fields.” Conventionally, only the concomitant field terms below the third order are considered significant. The spatial dependence and composition of the concomitant terms depend on the MRI gradient system design.
Conventional MRI gradient systems usually have cylindrical symmetric structure. The concomitant field for such systems contains only 2nd order spatial dependence. However, for asymmetric gradient systems, concomitant field terms with zeroth order and first order spatial dependence are also present. As a few examples, these zeroth and first order terms cause additional image shifts in standard echo planar imaging (“EPI”) sequences, echo shifts in diffusion imaging, and phase shifts in phase contrast imaging.
Various methods have been proposed for compensating the second order concomitant fields for symmetric gradient systems; however, for asymmetric gradient systems, the additional zeroth order and first order concomitant field terms are present and should be corrected.
For standard axial EPI, C. Meier, et al., proposed in “Concomitant Field Terms for Asymmetric Gradient Coils: Consequences for Diffusion, Flow, and Echo-Planar Imaging,” Magn. Reson. Med., 2008; 60:128-134, to add additional gradients in the z-direction to compensate for the first order self-squared terms (i.e., phase component exhibiting dependence on Gx2z or Gy2z) that only have linear spatial dependence in the z-direction. This approach does not address a more general case with arbitrary gradient combinations where the first order cross-terms (i.e., phase components exhibiting dependence on GxGzx, GxGzz, GyGzy, or GyGzz) and self-squared terms with other spatial dependencies (i.e., in x-direction and the y-direction, including Gz2x and Gz2y) are also present. Any adjustment to existent gradient waveforms would cause additional concomitant fields, which have not previously been considered.
Therefore, there remains a need to provide concomitant field correction and compensation for asymmetric gradient systems. Such correction and compensation techniques should be capable of addressing the full three-dimensional spatial dependency of the concomitant fields, and should avoid generating any secondary concomitant fields during the compensative correction process.